What is log_{10}((x^2y^4)/(z^3)) ?

The solution to log_{10}((x^2y^4)/(z^3)) is 2log_{10}(x)+4log_{10}(y)-3log_{10}(z)

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simplify log_{10}((x^2y^4)/(z^3))

simplify

lo g_{10} (\frac{x ^{2} y ^{4}}{z ^{3}})

2 lo g_{10} (x) + 4 lo g_{10} (y) - 3 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{2} y ^{4}}{z ^{3}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{x ^{2} y ^{4}}{z ^{3}}) = lo g_{10} (x^{2} y^{4}) - lo g_{10} (z^{3})

= lo g_{10} (x^{2} y^{4}) - lo g_{10} (z^{3})

lo g_{10} (x^{2} y^{4}) = 2 lo g_{10} (x) + 4 lo g_{10} (y)

lo g_{10} (z^{3}) = 3 lo g_{10} (z)

= 2 lo g_{10} (x) + 4 lo g_{10} (y) - 3 lo g_{10} (z)

ln (\frac{53}{7})

ln (11) - 3 ln (2)

lo g_{10} (x^{4} y^{5})

ln (1) + ln (15) + ln (120) + ln (680)

ln (x^{5}) - ln (x) + ln (\frac{1}{2})

What is log_{10}((x^2y^4)/(z^3)) ?
The solution to log_{10}((x^2y^4)/(z^3)) is 2log_{10}(x)+4log_{10}(y)-3log_{10}(z)